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MATH 135 (23)
Mike Eden (3)
Chapter

Integer Propositions

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Department
Mathematics
Course
MATH 135
Professor
Mike Eden
Semester
Fall

Description
List of All PropositionsSeptember25111140 PMTransitivity of Divisibility TDProofSince ab there exists an integer r so that rab 1Since bc there exists an integer s so that sbc 2Substituting ra for b in the previous equation we get sr ac 3Since sr is an integer ac4TopDivisibility of Integer Combinations DICSince ab there exists an integer k such that bka1Since ac there exists an integer l such that cla2Let x and y be any integers3Now bxcykaxlayakxly 4Since kxly Z it follows that abxcy5TopBounds By Divisibility BBDSince ab there exists an integer q so that bqa 1Since b 6 0 q 6 0 2But if q 6 0 q 1 3But then bqaqaa4TopDivision Algorithm DATopGreatest Common Denominator With Remainders GCD WR MATH 135 Page 1
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